How to design a tiny URL or URL shortener?

How to design a system that takes big URLs like “https://www.geeksforgeeks.org/count-sum-of-digits-in-numbers-from-1-to-n/” and converts them into a short 6 character URL. It is given that URLs are stored in the database and every URL has an associated integer id. 

One important thing to note is, the long URL should also be uniquely identifiable from the short URL. So we need a Bijective Function

We strongly recommend that you click here and practice it, before moving on to the solution.

One Simple Solution could be Hashing. Use a hash function to convert long string to short string. In hashing, that may be collisions (2 long URLs map to same short URL) and we need a unique short URL for every long URL so that we can access long URL back.

A Better Solution is to use the integer id stored in the database and convert the integer to a character string that is at most 6 characters long. This problem can basically seen as a base conversion problem where we have a 10 digit input number and we want to convert it into a 6-character long string. 

Below is one important observation about possible characters in URL.

A URL character can be one of the following 

1. A lower case alphabet [‘a’ to ‘z’], total 26 characters 
2. An upper case alphabet [‘A’ to ‘Z’], total 26 characters 
3. A digit [‘0’ to ‘9’], total 10 characters

There are total 26 + 26 + 10 = 62 possible characters.
So the task is to convert a decimal number to base 62 number. 
To get the original long URL, we need to get URL id in the database. The id can be obtained using base 62 to decimal conversion.

Implementation:

C++

// C++ program to generate short url from integer id and
// integer id back from short url.
#include<iostream>
#include<algorithm>
#include<string>
using namespace std;

// Function to generate a short url from integer ID
string idToShortURL(long int n)
{
    // Map to store 62 possible characters
    char map[] = "abcdefghijklmnopqrstuvwxyzABCDEF"
                 "GHIJKLMNOPQRSTUVWXYZ0123456789";

    string shorturl;

    // Convert given integer id to a base 62 number
    while (n)
    {
        // use above map to store actual character
        // in short url
        shorturl.push_back(map[n%62]);
        n = n/62;
    }

    // Reverse shortURL to complete base conversion
    reverse(shorturl.begin(), shorturl.end());

    return shorturl;
}

// Function to get integer ID back from a short url
long int shortURLtoID(string shortURL)
{
    long int id = 0; // initialize result

    // A simple base conversion logic
    for (int i=0; i < shortURL.length(); i++)
    {
        if ('a' <= shortURL[i] && shortURL[i] <= 'z')
          id = id*62 + shortURL[i] - 'a';
        if ('A' <= shortURL[i] && shortURL[i] <= 'Z')
          id = id*62 + shortURL[i] - 'A' + 26;
        if ('0' <= shortURL[i] && shortURL[i] <= '9')
          id = id*62 + shortURL[i] - '0' + 52;
    }
    return id;
}

// Driver program to test above function
int main()
{
    int n = 12345;
    string shorturl = idToShortURL(n);
    cout << "Generated short url is " << shorturl << endl;
    cout << "Id from url is " << shortURLtoID(shorturl);
    return 0;
}

Java

// Java program to generate short url from integer id and
// integer id back from short url.
import java.util.*;
import java.lang.*;
import java.io.*;

class GFG
{
    // Function to generate a short url from integer ID
    static String idToShortURL(int n)
    {
        // Map to store 62 possible characters
        char map[] = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789".toCharArray();

        StringBuffer shorturl = new StringBuffer();

        // Convert given integer id to a base 62 number
        while (n > 0)
        {
            // use above map to store actual character
            // in short url
            shorturl.append(map[n % 62]);
            n = n / 62;
        }

        // Reverse shortURL to complete base conversion
        return shorturl.reverse().toString();
    }

    // Function to get integer ID back from a short url
    static int shortURLtoID(String shortURL)
    {
        int id = 0; // initialize result

        // A simple base conversion logic
        for (int i = 0; i < shortURL.length(); i++)
        {
            if ('a' <= shortURL.charAt(i) &&
                       shortURL.charAt(i) <= 'z')
            id = id * 62 + shortURL.charAt(i) - 'a';
            if ('A' <= shortURL.charAt(i) &&
                       shortURL.charAt(i) <= 'Z')
            id = id * 62 + shortURL.charAt(i) - 'A' + 26;
            if ('0' <= shortURL.charAt(i) &&
                       shortURL.charAt(i) <= '9')
            id = id * 62 + shortURL.charAt(i) - '0' + 52;
        }
        return id;
    }

    // Driver Code
    public static void main (String[] args) throws IOException
    {
        int n = 12345;
        String shorturl = idToShortURL(n);
        System.out.println("Generated short url is " + shorturl);
        System.out.println("Id from url is " +
                            shortURLtoID(shorturl));
    }
}

// This code is contributed by shubham96301

Python3

# Python3 code for above approach
def idToShortURL(id):
    map = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789"
    shortURL = ""

    # for each digit find the base 62
    while(id > 0):
        shortURL += map[id % 62]
        id //= 62

    # reversing the shortURL
    return shortURL[len(shortURL): : -1]

def shortURLToId(shortURL):
    id = 0
    for i in shortURL:
        val_i = ord(i)
        if(val_i >= ord('a') and val_i <= ord('z')):
            id = id*62 + val_i - ord('a')
        elif(val_i >= ord('A') and val_i <= ord('Z')):
            id = id*62 + val_i - ord('A') + 26
        else:
            id = id*62 + val_i - ord('0') + 52
    return id

if (__name__ == "__main__"):
    id = 12345
    shortURL = idToShortURL(id)
    print("Short URL from 12345 is : ", shortURL)
    print("ID from", shortURL, "is : ", shortURLToId(shortURL))

C#

// C# program to generate short url from integer id and
// integer id back from short url.
using System;

public class GFG
{
    // Function to generate a short url from integer ID
    static String idToShortURL(int n)
    {
        // Map to store 62 possible characters
        char []map = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789".ToCharArray();

        String shorturl = "";

        // Convert given integer id to a base 62 number
        while (n > 0)
        {
            // use above map to store actual character
            // in short url
            shorturl+=(map[n % 62]);
            n = n / 62;
        }

        // Reverse shortURL to complete base conversion
        return reverse(shorturl);
    }
    static String reverse(String input) {
        char[] a = input.ToCharArray();
        int l, r = a.Length - 1;
        for (l = 0; l < r; l++, r--) {
            char temp = a[l];
            a[l] = a[r];
            a[r] = temp;
        }
        return String.Join("",a);
    }
    // Function to get integer ID back from a short url
    static int shortURLtoID(String shortURL)
    {
        int id = 0; // initialize result

        // A simple base conversion logic
        for (int i = 0; i < shortURL.Length; i++)
        {
            if ('a' <= shortURL[i] &&
                       shortURL[i] <= 'z')
            id = id * 62 + shortURL[i] - 'a';
            if ('A' <= shortURL[i] &&
                       shortURL[i] <= 'Z')
            id = id * 62 + shortURL[i] - 'A' + 26;
            if ('0' <= shortURL[i] &&
                       shortURL[i] <= '9')
            id = id * 62 + shortURL[i] - '0' + 52;
        }
        return id;
    }

    // Driver Code
    public static void Main(String[] args)
    {
        int n = 12345;
        String shorturl = idToShortURL(n);
        Console.WriteLine("Generated short url is " + shorturl);
        Console.WriteLine("Id from url is " +
                            shortURLtoID(shorturl));
    }
}

// This code is contributed by 29AjayKumar

Javascript

<script>
// Javascript program to generate short url from integer id and
// integer id back from short url.

// Function to generate a short url from integer ID
function idToShortURL(n)
{

    // Map to store 62 possible characters
    let map = "abcdefghijklmnopqrstuvwxyzABCDEF"
    "GHIJKLMNOPQRSTUVWXYZ0123456789";

    let shorturl = [];

    // Convert given integer id to a base 62 number
    while (n)
    {
        // use above map to store actual character
        // in short url
        shorturl.push(map[n % 62]);
        n = Math.floor(n / 62);
    }

    // Reverse shortURL to complete base conversion
    shorturl.reverse();

    return shorturl.join("");
}

// Function to get integer ID back from a short url
function shortURLtoID(shortURL) {
    let id = 0; // initialize result

    // A simple base conversion logic
    for (let i = 0; i < shortURL.length; i++) {
        if ('a' <= shortURL[i] && shortURL[i] <= 'z')
            id = id * 62 + shortURL[i].charCodeAt(0) - 'a'.charCodeAt(0);
        if ('A' <= shortURL[i] && shortURL[i] <= 'Z')
            id = id * 62 + shortURL[i].charCodeAt(0) - 'A'.charCodeAt(0) + 26;
        if ('0' <= shortURL[i] && shortURL[i] <= '9')
            id = id * 62 + shortURL[i].charCodeAt(0) - '0'.charCodeAt(0) + 52;
    }
    return id;
}

// Driver program to test above function

let n = 12345;
let shorturl = idToShortURL(n);
document.write("Generated short url is " + shorturl + "<br>");
document.write("Id from url is " + shortURLtoID(shorturl));

// This code is contributed by gfgking.
</script>

Output

Generated short url is dnh
Id from url is 12345

Time complexity : O(n) 
Auxiliary Space : O(1)

Optimization: We can avoid reverse step in idToShortURL(). To make sure that we get the same ID back, we also need to change shortURLtoID() to process characters from the end instead of the beginning.